Newsfeeds are known as RSS.
There is some discussion as to what RSS stands for, but most people plump for 'Really Simple Syndication'.
In essence, the feeds themselves are just web pages, designed to be read by computers rather than people.
The first thing you need is something called a news reader. This is a piece of software that checks the feeds and lets you read any new articles that have been added. There are many different versions, some of which are accessed using a browser, and some of which are downloadable applications.
Some browsers like Firefox or Safari have an inbuilt RSS reader capability
If you click on the RSS button you can subscribe to the feed in various ways, including by dragging the URL of the feed into your news reader or by cutting and pasting the same URL into a new feed in your news reader. Most sites that offer feeds use a similar orange button, but some may just have a normal web link.
Some browsers, including Firefox, Opera and Safari, automatically check for feeds for you when you visit a website, and display an icon when they find one. This can make subscribing to feeds much easier.